Following [1]}, a ring \(R\)  is said to be a purified ring if for every distinct minimal prime ideals \(\mathfrak {p}\)  and \(\mathfrak {p}^{\prime }\) 
of \(R\) , there exists an idempotent \(e\)  of \(R\)  such that \(e\in \mathfrak {p}\)  and \(1-e\in \mathfrak {p}^{\prime }\) . Note that every purified ring is an mp-ring.
